Optimizing Thermodynamic Models: The Relevance of Molar Fraction Uncertainties

Parameters contained in thermodynamic models are usually optimized over vapor-liquid equilibrium data of binary systems, applying methods that enable consideration of the uncertainty of experimental data, such as the Maximum Likelihood Method (MLM). However, authors of these data generally indicate only the maximum or average uncertainty associated with an overall set of data. Specific uncertainties, associated with each measurement, are rarely mentioned. As a consequence, the optimization of models by, for example, MLM is usually performed by associating constant overall uncertainty values to data points, instead of their specific values. This paper aims to show that results obtained from the application of MLM are strongly affected by the use of constant rather than specific uncertainties. In particular, the optimization of models over highly nonideal high-pressure vapor-liquid equilibrium data is strongly affected by the uncertainty of molar fractions, rather than by the uncertainty of pressure and temperature measurements. In this paper, these concepts will be stressed by practical examples, showing how the use of constant rather than composition-dependent molar fraction uncertainties may affect the computation of molar fraction variances and covariances incorporated in the maximum likelihood objective function. Also, a simple methodology for the estimation of the uncertainties of molar fractions measured by gas-chromatographic measurements is presented and specifically applied to the considered systems. This methodology could conveniently be applied to estimate the composition-dependent uncertainty of literature data for which authors only specified either the maximum or the average molar fraction uncertainty of the whole set of data.